We consider a discrete time branching random walk where each particle splits into two at integer times and the offspring move independently by a normal random variable. We introduce a penalty that penalises particles that get within a distance epsilon of each other. We analyse the most likely configurations of particles under the tilted measure for a fixed time horizon N. It turns out that spread very quickly to a distance 2^{2N/3} and show a very abrupt change in behaviour at time 2N/3. 

This is joint work with Lisa Hartung, Frank den Hollander and Stefan Müller.